TLDR version:
1) It actually takes a pretty good headphone to respond well to EQ without causing it to lose soundstage and resolving ability. And it especially takes a really good EQ.
2) EQ can't improve detail resolution and sound stage (seeing point one, it can really only make it worse).
You can think of headphones having a few primary characteristics on a physics level that play out in different ways:
1) the ability of the driver to move quickly enough to reproduce the source accurately as possible.
2) the ability of the driver to equally provide the same force across the spectrum.
3) The enclosure's resonances
4) the degree to which the two parts are matched
How these interplay create 90% of the headphone's characteristics.
One aspect of the resulting sound is frequency response. That is the degree to which a headphone sounds bassy, or neautral, or midrange heavy, or whatever else. It's the easiest aspect of a headphone to characterize, and many refer to this as the headphone's "sound signature." EQ can certainly level the playing ground here a lot, especially a really good EQ. However, EQ shouldn't be looked at as a "fixer of cheap headphones" for several reasons. First, to get a good one, good enough to accurately get back to the sound signature you're after, it will often cost more than simply buying the headphone sound you're after int he first place. Secondly, often times as you push a mediocre to headphone in ways it isn't adept, bigger issues come to the fore. For instance, if you try to EQ in significant bass to the KSC75s, they can't handle this additional power load very well, and they just get indistinct and sound like skullcandys. So, ultimately, those headphones that are best able to handle an EQ adjustment with ease are, unfortunately, the headphones you don't really need to EQ in the first place. I have a pretty good EQ unit in my home system, and when it's in front of my amp and Grado SR225s, I can reshape the Grado's sound pretty easily, with little/no loss in sound quality. But if I try to put an EQ in front of my unamped KSC75s, as soon as I make almost any adjustments with the EQ, things start to fall apart. The KSC75s lose their definition, the sound stage narrows, bass gets muddy. Same when I try to EQ more bass into my AT AD700s, they just can't deal with it, and all the reasons I liked the headphone in the first place, the soundstage and detail resolution, fall apart in a hurry. I'm a believer that almost all headphones should be EQ tuned, based on both the headphone, but also your own personal ear characteristics. But that isn't a license to expect miracles from mediocre gear, if anything doing this is actually requires better gear, not worse.
Now, even if you do get a headphone and EQ it up, and it works out alright, that isn't all there is to a headphone either. There's also detail resolution and soundstage. Detail resolution is a combination of the driver's speed and internal resonances. You aren't fixing those at all with EQ. Soundstage has to do with how well the drivers are matched, how they are angled at your ear, and the frequency response at the upper ultra high frequencies (and the headphone's ability to enhance or dull quick contrasts in these ultra high frequencies). Again, EQ is of little/no use here. To some degree you can bring a headphone "forward" or "back in soundstage with an incredible EQ adjusting the ultra high frequencies, the so called presence frequencies, but you can do very little to make it wider, which usually has to do with resonances, enclosure symmetry and driver matching